1. Field of Invention
The present invention relates to an optical system and exposure apparatus having the optical system, and in particular to a projection optical system which is suitable for an exposure apparatus to be used to manufacture microdevices such as semiconductor devices and liquid crystal display devices using photolithography techniques.
2. Description of Related Art
It is known to use a method in which a pattern of a photomask (also called a reticle), which is etched therein by proportionally magnifying, 4-5 fold, the pattern to be formed on an electronic device (a microdevice) such as a semiconductor integrated circuit or a liquid crystal display, is reduced, exposed and formed onto a photosensitive substrate (an exposed substrate) such as a wafer. In this type of projection exposure apparatus, the exposure wavelength continues to shift towards shorter wavelengths in order to cope with the trend toward forming finer semiconductor integrated circuits.
Currently, a KrF excimer laser having an exposure wavelength of 248 nm is mainly used, but ArF excimer lasers with a shorter wavelength of 193 nm are beginning to be commercialized. Moreover, projection exposure apparatus using a light source which provides a beam in the wavelength band of the so-called vacuum ultraviolet region such as F2 laser with 157 nm wavelength, Kr2 laser with 146 nm wavelength and Ar2 laser having 126 nm wavelength are being proposed. Moreover, high resolution through larger numerical aperture (NA) of a projection optical system is being achieved, and development of an optical projection system having a larger numerical aperture, in addition to development of shorter wavelength for exposure, is being conducted.
The availability of optical material (lens material) having an excellent transmission rate and uniform property for exposure beam of short wavelength in the ultraviolet region is limited. In a projection optical system with an ArF excimer laser as a light source, synthetic silica glass may be used as a lens material, but with only one type of lens material, correction of chromatic aberration cannot be achieved sufficiently. Hence, calcium fluoride crystal (fluorite) is used for some of the lenses. On the other hand, in a projection optical system using an F2 laser as a light source, in reality, calcium fluoride crystal (fluorite) is the only lens material suitable for use.
Recently, the existence of intrinsic birefringence in cubic (isometric) system calcium fluoride crystal (fluorite) for such ultraviolet light with short wavelength has been reported. In a super high precision optical system such as a projection optical system used in manufacturing of electronic devices, aberration generated in conjunction with birefringence of the lens material is fatal, and the use of a lens composition and lens design substantially avoiding the effect of birefringence is crucial.
Considering the aforementioned problems, the present invention aims to assure excellent optical performance substantially without suffering the effect of birefringence even if a crystal material with intrinsic birefringence such as fluorite is used. In addition, the present invention aims to provide a microdevice production method enabling production of high performance microdevices, based on high resolution exposure technology, using an exposure apparatus in which a projection optical system having excellent optical performance utilizing crystal material is provided.
In order to address the aforementioned problems, a first aspect of the present invention provides an optical system having a plurality of crystal optical elements formed with cubic system crystals, wherein the plurality of crystal optical elements comprise first crystal optical elements having a first crystal axis that substantially coincides with an optical axis of the optical system, and second crystal optical elements having a second crystal axis that is different from the first crystal axis, and that is disposed to substantially coincide with the optical axis. The plurality of crystal optical elements Gj are arranged in such a manner that a direction of a predetermined crystal axis in a surface perpendicular to the optical axis is rotated xcfx81j around the optical axis relative to the direction of a predetermined axis in the surface. For a specific light beam passing through the plurality of crystal optical elements Gj, a first evaluation amount Rj for a first predetermined polarization and a second evaluation amount Sj for a second predetermined polarization which are determined by a material constant a of the crystal, the crystal axis substantially coinciding with the optical axis, an angle xcfx81j, an angle xcex8j, an angle "PHgr"j and an optical path length Lj are established, where xcex8j is an angle between the specific light beam and the direction of the optical axis, "PHgr"j is an angle between the specific light beam and the direction of the predetermined axis, and Lj is the optical path length of the specific optical path. In addition, a first sum of evaluation amounts xcexa3Rj which is a sum of the first evaluation amount Rj for the plurality of crystal optical elements and a second sum of evaluation amounts xcexa3Sj which is a sum of the second evaluation amount Sj for the plurality of crystal optical elements have a predetermined relationship for light beams in imaging beams converged on at least one arbitrary point on an image plane or an object plane of the optical system.
In a preferred embodiment of the first aspect of the invention, the first evaluation amount Rj is information concerning a change in optical path length for the first predetermined polarization, and the second evaluation amount Sj is information concerning a change in optical path length for the second predetermined polarization. In addition, the first predetermined polarization is preferably R polarization having a polarization direction in the radial direction with the center at the optical axis, and the second predetermined polarization is preferably xcex8 polarization having a polarization direction in the tangential direction with the center at the optical axis. Furthermore, the predetermined relationship preferably includes a relationship in which the first sum of evaluation amounts Rj is substantially equal for light beams in imaging beams converged on at least one arbitrary point on the image plane or the object plane of the optical system, the second sum of evaluation amounts xcexa3Sj is substantially equal for light beams in imaging beams converged on at least one arbitrary point on the image plane or the object plane of the optical system, and the first sum of the evaluation amounts Rj and the second sum of the evaluation amounts Sj are substantially equal to each other for light beams in imaging beams converged on at least one arbitrary point on the image plane or the object plane of the optical system.
In a preferred embodiment of the first aspect of the invention, the first evaluation amount Rj and the second evaluation amount Sj are represented by the following equations, and the crystal optical elements Gj are set in such a manner that the optical axis substantially coincides with the crystal axis [111] or a crystal axis optically equivalent thereto, and the predetermined crystal axis is the crystal axis [xe2x88x92110] or a crystal axis optically equivalent thereto:
[Equations 3]
Rj=xcex1xc3x97Ljxc3x97[56xc3x97{1xe2x88x92cos(4xcex8j)}xe2x88x92322xc3x97sin(4xcex8j)xc3x97sin(3xcfx89j)]/192 
Sj=xcex1xc3x97Ljxc3x97[32xc3x97{1xe2x88x92cos(2xcex8j)}+642xc3x97sin(2xcex8j)xc3x97sin(3xcfx89j)]/192, 
where xcfx89j="PHgr"jxe2x88x92xcfx81j.
In a preferred embodiment of the first aspect of the invention, the first evaluation amount Rj and the second evaluation amount Sj are represented by the following equations, and the crystal optical elements Gj are disposed in such a manner that the optical axis substantially coincides with the crystal axis [001] or a crystal axis optically equivalent thereto, and the predetermined crystal axis is the crystal axis [110] or a crystal axis optically equivalent thereto:
Rj=xcex1xc3x97Ljxc3x97{1xe2x88x92cos(4xcex8j)}xc3x97(xe2x88x9284xe2x88x9212xc3x97cos(4xcfx89j))/192 
Sj=xcex1xc3x97Ljxc3x97{1xe2x88x92cos(2xcex8j)}xc3x97(xe2x88x9248+48xc3x97cos(4xcfx89j))/192 
where xcfx89j="PHgr"jxe2x88x92xcfx81j.
In a preferred embodiment of the first aspect of the invention, the first evaluation amount Rj and the second evaluation amount Sj are represented by the following equations, and the crystal optical elements Gj are disposed in such a manner that the optical axis substantially coincides with the crystal axis [011] or a crystal axis optically equivalent thereto, and the predetermined crystal axis is the crystal axis [100] or a crystal axis optically equivalent thereto:
[Equations 4]
Rj=xcex1xc3x97Ljxc3x97[{1xe2x88x92cos(4xcex8j)}xc3x97{21xe2x88x929xc3x97cos(4xcfx89j)xe2x88x9284xc3x97cos(2xcfx89j)}+96xc3x97cos(2xcfx89j)]/192 
Sj=xcex1xc3x97Ljxc3x97[{1xe2x88x92cos(2xcex8j)}xc3x97{12+36xc3x97cos(4xcfx89j)+48xc3x97cos(2xcfx89j)}xe2x88x9296xc3x97cos(2xcfx89j)]/192 
where xcfx89j="PHgr"jxe2x88x92xcfx81j.
In a preferred embodiment of the first aspect of the invention, the material constant a of the crystal is a difference between a refractive index n100 of the light beam having a polarization direction in the direction of the crystal axis [100] or a crystal axis optically equivalent thereto, and a refractive index n011 of the light beam having a polarization direction in the direction of the crystal axis [0-11] or a crystal axis optically equivalent thereto, out of light beams advancing in the direction of the crystal axis [011] or a crystal axis optically equivalent thereto, out of all crystals forming each crystal optical element Gj. In addition, the absolute value of the difference between the first sum of evaluation amounts xcexa3Rj and the second sum of evaluation amounts xcexa3Sj is preferably set to be smaller than xcex/2 for light beams in imaging beams converged on at least one arbitrary point on the image plane or the object plane of the optical system, where xcex is the wavelength of the light beam.
In a preferred embodiment of the first aspect of the invention, the absolute value of the difference between the first sum of evaluation amounts xcexa3Rj and a predetermined value is preferably set to be smaller than xcex/2 for light beams in imaging beams converged on the at least one arbitrary point on the image plane or the object plane of the optical system, where xcex is the wavelength of the light beam. In addition, the absolute value of the difference between the second sum of evaluation amounts xcexa3Sj and the predetermined value is preferably set to be smaller than xcex/2 for light beams in imaging beams converged on the at least one arbitrary point on the image plane or the object plane of the optical system, where xcex is the wavelength of the light beam.
Furthermore, in a preferred embodiment of the first aspect of the invention, the optical system includes M (M is a whole number greater than or equal to 3) crystal optical elements disposed in such a manner that their optical axis substantially coincides with the crystal axis [111] or a crystal axis optically equivalent thereto, and wherein the M crystal optical elements have a rotational position relationship in which the directions of the crystal axis [1-10] or a crystal axis optically equivalent thereto are mutually separated by substantially (120/M) degrees in the surface perpendicular to the optical axis.
Furthermore, in a preferred embodiment of the first aspect of the invention, the optical system includes N (N is a whole number greater than or equal to 3) crystal optical elements disposed in such a manner that their optical axis substantially coincides with the crystal axis [001] or a crystal axis optically equivalent thereto, and wherein the N crystal optical elements have a rotational position relationship in which the directions of the crystal axis [100] or a crystal axis optically equivalent thereto are mutually separated by substantially (90/N) degrees in the surface perpendicular to the optical axis.
In addition, in a preferred embodiment of the first aspect of the invention, the optical system includes L (L is a whole number greater than or equal to 3) crystal optical elements disposed in such a manner that their optical axis substantially coincides with the crystal axis [011] or a crystal axis optically equivalent thereto, and wherein the L crystal optical elements have a rotational position relationship in which the directions of the crystal axis [100] or a crystal axis optically equivalent thereto are mutually separated by substantially (180/L) degrees in the surface perpendicular to the optical axis.
Furthermore, in a preferred embodiment of the first aspect of the invention, the optical system includes P (P is a whole number greater than or equal to 2) crystal optical elements disposed in such a manner that their optical axis substantially coincides with the crystal axis [011] or a crystal axis optically equivalent thereto, and wherein the P crystal optical elements have a rotational position relationship in which the directions of the crystal axis [100] or a crystal axis optically equivalent thereto are mutually separated by substantially (90/P) degrees in the surface perpendicular to the optical axis.
A second aspect of the present invention provides an optical system having a plurality of crystal optical elements formed with cubic system crystals, wherein M (M is a whole number greater than or equal to 3) crystal optical elements are disposed in such a manner that their optical axis substantially coincides with the crystal axis [111] or a crystal axis optically equivalent thereto, and wherein the M crystal optical elements have a rotational position relationship in which the directions of the crystal axis [1-10] or a crystal axis optically equivalent thereto are mutually separated by substantially (120/M) degrees in the surface perpendicular to the optical axis.
A third aspect of the present invention provides an optical system having a plurality of crystal optical elements formed with cubic system crystals, wherein N (N is a whole number greater than or equal to 3) crystal optical elements are disposed in such a manner that their optical axis substantially coincides with the crystal axis [001] or a crystal axis optically equivalent thereto, and wherein the N crystal optical elements have a rotational position relationship in which the directions of the crystal axis [100] or a crystal axis optically equivalent thereto are mutually separated by substantially (90/N) degrees in the surface perpendicular to the optical axis.
A fourth aspect of the present invention provides an optical system having a plurality of crystal optical elements formed with cubic system crystals, wherein L (L is a whole number greater than or equal to 3) crystal optical elements are disposed in such a manner that their optical axis substantially coincides with the crystal axis [011] or a crystal axis optically equivalent thereto, and wherein the L crystal optical elements have a rotational position relationship in which the directions of the crystal axis [100] or a crystal axis optically equivalent thereto are mutually separated by substantially (180/L) degrees in the surface perpendicular to the optical axis.
A fifth aspect of the present invention provides an optical system including P (P is a whole number greater than or equal to 2) crystal optical elements disposed in such a manner that their optical axis substantially coincides with the crystal axis [011] or a crystal axis optically equivalent thereto, and wherein the P crystal optical elements have a rotational position relationship in which the directions of a crystal axis [100] or the crystal axis optically equivalent thereto are mutually separated by substantially (90/P) degrees in the surface perpendicular to the optical axis. In the first-fifth aspects of the invention, each of two or more crystal optical elements are preferably made to possess a rotational error of no more than xc2x14 degrees, or the angle error between the optical axis and the crystal axis which should coincide with the optical axis of no more than xc2x14 degrees.
In one preferred embodiment of the first-fifth aspects of the invention, the crystal is preferably either a calcium fluoride crystal or a barium fluoride crystal. In addition, at least one concave surface reflection mirror is preferably provided. Furthermore, optimum aberration correction is preferably executed for the oscillation wavelength of an ArF excimer laser, or for the oscillation wavelength of an F2 laser.
A sixth aspect of the present invention provides an exposure apparatus comprising an illumination system for illuminating a mask and an optical system of the first-fifth aspects of the invention for forming images of a pattern formed on the mask onto a photosensitive substrate.
A seventh aspect of the present invention provides a microdevice production method comprising an exposure step of exposing a pattern of a mask onto a photosensitive substrate using the exposure apparatus of the sixth aspect of the invention, and a development step of developing the exposed photosensitive substrate.